# Get highest y-axis point of quadratic graph

Hi..

-2x^2 + 5x + 7 = 0

With the help of you lot, I've solved 'x', like so:

x = -1
or
x = 7 / 2

Now, I need to find the *highest*point of the graph (in terms of the y-axis)... Do I need to use trial and error for this? Or can it be solved via algebra?

Regards;
LVL 25
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Commented:
You know two values of x where y = 0.  The hightest point will occur exactly halfway between the two.
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Author Commented:
Of course!! So simple!  :-)
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Author Commented:
..Thank you!
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Commented:
InteractiveMind,

snoyes jw gave an ingenious method.  Perhaps you would like to know another method.

Can you differentiate?  (If not, ignore this comment entirely.)  We're looking for an extremum of the parabola, in other words, a place where the slope is zero.  So the first derivative should equal zero.
Let f(x) = -2x^2 + 5x + 7
Then f'(x) = -4x + 5
Now we can set this equal to zero and solve for x.

mathbiol
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